Abstract
Formality is a topological property that arises from the rational homotopy theory developed by Quillen and Sullivan in 70's. Roughly speaking, the rational homotopy type of a formal space is determined by its cohomology algebra. In this thesis, we explore the graded-formality, filtered-formality, and 1-formality of finitely-generated groups, by studying various Lie algebras over a field of characteristic 0 attached to such groups, including the associated graded Lie algebra, the holonomy Lie algebra, and the Malcev Lie algebra. We explain how these notions behave with respect to split injections, coproducts, direct products, and how they are inherited by solvable and nilpotent quotients.
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